This application claims the priority of German Patent Application, Serial No. 101 63 503.6, filed Dec. 21, 2001, pursuant to 35 U.S.C. 119(a)-(d), the disclosure of which is incorporated herein by reference.
The present invention relates to a method and a numerical controller for guiding a motion of a movable machine element of a numerically controlled industrial processing machine, such as a machine tool, a robot and the like.
The orientation of tools used in industrial processing machines, for example machine tools with continuous kinematical orientation of tools in space, is typically programmed for each set. For example, the tool orientation can be programmed either directly by indicating the rotation axes positions. Alternatively, a more elegant method includes programming the orientation of the tool in space by way of orientation vectors.
In typical situations, an orientation is programmed in each NC set that is to be attained at the end of the set. The orientation is typically changed between the start vector and the end vector by a great circle interpolation, i.e., the orientation vector is rotated in a plane spanned by the start vector and the end vector. The angle relative to the start vector is hereby linearly interpolated.
When the orientations are interpolated with a great circle interpolation over several consecutive sets, the orientation vector typically changes its direction abruptly at the transitions between sets. This causes discontinuous changes in the velocity and acceleration of the rotation axes at the transitions between sets. This means that the great circle integration is not able to generate a motion with a constant velocity and acceleration of the orientation axes over several sets.
This situation occurs for normal linear axes, when only G1 sets are interpolated. A motion with a continuous acceleration can be achieved with the linear axes if polynomials are used for interpolating the axes. However, a method used with linear axes cannot easily be applied to orientations without taking into account the special properties of the orientation vectors. Moreover, even with xe2x80x9cnormalxe2x80x9d axis interpolation, polynomials can also be programmed for the axes motion in addition linear sets and circles. This allows complex geometries to be programmed. However, such a such an interpolation method cannot be applied to orientation vectors.
It would therefore be desirable and advantageous to provide an improved control method to obviate prior art shortcomings and capable of programming polynomials for changing orientation vectors. It would further be desirable and advantageous to provide a motion of the orientation axes with continuous velocity and continuous acceleration over several sets.
According to one aspect of the invention, a control method for guiding a motion of a movable machine element of a numerically controlled industrial processing machine is provided that includes the steps of orienting the machine element in a workspace using orientation vectors, subdividing an orientation and a motion path of the machine element into a plurality of sequential contiguous motion segments, changing the orientation of the machine element within a motion segment by tilting an orientation vector from a start vector to an end vector about a first angle in a plane spanned by the start vector and end vector and about a second angle perpendicular to that plane, and interpolating the first and second angles of orientation vectors over several motion segments.
In this way, an orientation vector can be programmed in each set, wherein the orientation vector can be arrived at via a great circle interpolation (i.e., a linear interpolation of the angle in the plane which is spanned by the start actor and the end vector). The programming polynomials can define an almost arbitrary xe2x80x9cpathxe2x80x9d by which this end vector can be attained. In a more general case, the interpolated orientation vector is no longer located in the plane between the start vector and the end vector, but can be rotated arbitrarily out of this plane.
According to another feature of the present invention, the two angles of the orientation vectors may be interpolated by a polynomial interpolation over several motion segments. The constant and the linear efficient of a polynomial for the polynomial interpolation can be defined by the start value or end value of an orientation vector.
The angles of orientation vectors can also be interpolated over several motion segments by a spline interpolation.
A method according to the present invention can be suitably applied to a movable machine element implemented as a tool of a processing machine wherein the orientation vector describes a curve of the tool tip in space.
In the aforedescribed great circle interpolation, the tool orientation is interpolated in a plane spanned by the start orientation and the end orientation. The orientation vector can be tilted out of this plane by programming additional polynomials according to the invention. However, even this type of interpolation can only approximately interpolate the orientation vector on a conical surface.
Such orientation changes cannot be interpolated in a single set, and sets will typically have to be subdivided depending on the desired accuracy. This results in consecutive, typically short sets, wherein the orientation change is interpolated via great circle interpolation. In addition, these orientation changes can be smoothed, so that overall a smooth orientation curve can be achieved. However, the orientation changes required when which machining, for example, a circular contour with a constant tool setting angle (inclination), still cannot be described exactly. The orientation vectors are here interpolated over several motion segments, in the same manner circles are interpolated in a plane.
With the enhanced orientation interpolation according to the invention, orientation changes can be described on a conical surface with an arbitrary location/orientation in space. Hereby, a first angle may represent a rotation angle of an orientation about the center axis of the cone and a second angle may represent the apex angle. Accordingly, the coefficients of the polynomials or splines for interpolating an orientation of the machine element can be selected so that the motion of the orientation axes of the machine element has a continuous velocity and/or continuous acceleration.
The method of the invention can be carried out with a suitably programmed numerical controller.